1.17.5 problem 5

Internal problem ID [518]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 03:59:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 36 x^{2} y^{\prime \prime }+60 x y^{\prime }+\left (9 x^{3}-5\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 27

ode:=36*x^2*diff(diff(y(x),x),x)+60*x*diff(y(x),x)+(9*x^3-5)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \operatorname {BesselJ}\left (\frac {1}{3}, \frac {x^{{3}/{2}}}{3}\right )+c_2 \operatorname {BesselY}\left (\frac {1}{3}, \frac {x^{{3}/{2}}}{3}\right )}{x^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 44

ode=36*x^2*D[y[x],{x,2}]+60*x*D[y[x],x]+(9*x^3-5)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 \operatorname {AiryAi}\left (\frac {\sqrt [3]{-1} x}{2^{2/3}}\right )+c_2 \operatorname {AiryBi}\left (\frac {\sqrt [3]{-1} x}{2^{2/3}}\right )}{x^{5/6}} \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*x**2*Derivative(y(x), (x, 2)) + 60*x*Derivative(y(x), x) + (9*x**3 - 5)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} J_{\frac {1}{3}}\left (\frac {x^{\frac {3}{2}}}{3}\right ) + C_{2} Y_{\frac {1}{3}}\left (\frac {x^{\frac {3}{2}}}{3}\right )}{\sqrt [3]{x}} \]